The man arrested in France on suspicion of killing three people at Brussels' Jewish Museum has been carrying a Kalashnikov wrapped in a flag with the inscriptions of a militant Islamist group, prosecutors said.

Mehdi Nemmouche, carried the flag of the Islamic State of Iraq and the Levant (ISIL), an ultra-conservative militant group reconstituted from an earlier incarnation of al Qaeda and active in Syria and Iraq.

The 29-year-old Frenchman is said to have returned recently from fighting with Islamist militant rebels in Syria, prosecutors said.

French police have arrested a 29-year-old man suspected of being involved in the shooting deaths last weekend of three people at Brussels' Jewish Museum, official sources in Belgium and France said on Sunday.

A family lights candles at the Jewish Museum, site of a shooting in central Brussels. Credit: Reuters

Belgian police are still hunting a gunman who shot dead two Israelis and a French woman at the Jewish Museum in Brussels, in an attack thought to be motivated by anti-Semitism.

Security around all Jewish institutions in Belgium was raised to the highest level following Saturday's shooting, while French authorities stepped up security after two Jews were attacked near a Paris synagogue.